(CNN) -- Qantas, Australia's national airline, grounded its Airbus A380 fleet indefinitely after one of its planes suffered a midair engine failure on Thursday.

The airline said flights of the twin-deck planes -- the world's largest airliners -- will remain suspended until an investigation into Thursday's incident is complete.

"As long as it takes," said airline CEO Alan Joyce, when a reporter asked how long the suspension would last. "We are being very cautious until we know exactly what caused this."

One of the four engines on a Qantas airliner shut down six minutes after takeoff Thursday from Singapore's Changi Airport, Joyce said. The plane -- with 440 passengers and 26 crew members -- was headed to Sydney, Australia, but it returned to Changi.

While in the air above the western Indonesian island of Batam, part of the engine's covering, or cowling, tore off.

"I am not sure what actually happened with the debris and why parts of the engine left the aircraft and fell into the ground," Joyce said. "We're still looking at what exactly was the cause of that."

"I do apologize," the pilot said. "I'm sure you are aware we have a technical issue with our number two engine. We have dealt with the situation, the aircraft is secure at this stage. We're going to have to hold for some time whilst we do lighten our load by dumping some fuel and a number of checklist [items] we have to perform.

"I'm sure you are aware we are not proceeding to Sydney at this stage. We're making a left turn now to track back toward Singapore and as we progress with this we'll keep you informed, but at this stage everything is secure, the aircraft is flying safely and we'll get back to you very shortly with further information. Thank you for your patience."

Local television stations in Indonesia showed debris parts with red-white markings. Pictures of the Airbus A380 after it landed showed the cowling torn off in the back half.

Trifuadi, a security officer at an engineering firm in Batam, said he heard a loud explosion and saw smoke coming out of the engine of a plane flying overhead.

Shortly afterward, debris fell from the plane to the ground, said Trifuadi who, like many Indonesians, goes by one name.

The flight -- QF32 -- landed in Singapore safely, without injury to passenger or crew.

Passenger Meg Graham said she heard a loud bang within minutes of the plane taking off. "And then another bang," she said.

Ulf Waschbusch, who said he was on his way to Australia for the first time, said the crew kept passengers apprised of what was happening.

"We all stayed pretty calm," he told CNN. "It was an almost eerie calm."

The airline said it will work with the plane's manufacturer as well as Rolls-Royce, the maker of the engine, to determine what went wrong. A spokesman for the Rolls-Royce told CNN that "safety is always our highest priority. We are currently analyzing the available information and working with our customers to support their operations."

Qantas now has six A380s in its fleet of 191 planes. Airbus will at some point deliver another 14, the airline said.

Singapore Airlines announced Thursday that it has temporarily halted flights of its 11 Airbus A380s to do precautionary checks in light of the Qantas incident.

Lufthansa, which operates three Airbus A380s, told CNN it is planning to carry out additional precautionary checks on the engines of the planes. The airline is waiting for more detail from Rolls-Royce about the specific checks that need to be carried out before they proceed.